Perception, 2007, volume 36, pages 1049 ^ 1056
doi:10.1068/p5529
Relationship between frames of reference and mirror-image
reversals
Hirokazu Yoshimura
Department of Psychology, Hosei University, 2-17-1 Fujimi, Chiyoda-ku, Tokyo 102-8160, Japan;
e-mail: yosimura@hosei.ac.jp
Tatsuo Tabata
Osaka Prefecture University, Sakai, Osaka, Japan; also Institute for Data Evaluation and Analysis,
Sakai, Osaka, Japan
Received 1 August 2005, in revised form 8 September 2006
Abstract. The mirror puzzle related to the perception of mirror images as left ^ right reversed
can be more fully understood by considering an extended problem that includes also the perception of mirror images that are not left ^ right reversed. The purpose of the present study is
to clarify the physical aspect of this extended problem logically and parsimoniously. Separate
use of the intrinsic frame of reference that belongs to the object and one that belongs to its
mirror image always leads to the perception of left ^ right reversal when the object has left ^ right
asymmetry; on the other hand, the perception of left ^ right nonreversal is always due to the
application of a common frame of reference to the object and its mirror image.
1 Introduction
Many authors have attempted to solve the mirror puzzle: ``Why does the mirror reverse
left and right, but not up and down?'' (eg see the review by Gregory 1997), and the
final solution seems to have been provided by Corballis (2000), Tabata and Okuda
(2000), and McManus (2002) so long as the puzzle is restricted to the above question.
However, one does not always perceive the mirror image as left ^ right reversed; sometimes
it is perceived as reversed in the front ^ back or top ^ bottom direction, or as reversed in no
direction at all (these latter three cases are called here left ^ right nonreversal). To understand the perception of mirror images completely, it is important to consider the extended
mirror problem that includes both left ^ right reversal and nonreversal.
Psychological processes are involved in the perception of mirror images, but factors
not related to these processes should be separated in analysing the extended mirror
problem. In fact, Tabata and Okuda (2000) argued that the solution to the original
mirror puzzle can be given essentially without recourse to psychology. In the present
paper we give an explanation for the nonpsychological or physical aspect of the extended
mirror problem to provide a basis for better understanding of the perception of mirror
images.
2 Physical aspect of mirror reflection
The mechanism of mirror reflection is explained by geometrical optics as follows:
A mirror reverses the axis perpendicular to the mirror plane, ie a mirror produces
a plane-symmetric image of an object with respect to the mirror (eg Southall 1933/
1964). In other words, an object and its mirror image are enantiomorphic to each
other (eg Gardner 1964, 1990). An enantiomorph is defined as the object produced by
reversing an asymmetric object along one or all three orthogonal axes. Left and right
hands are typical examples of enantiomorphs.
We can treat the physical aspect of the extended mirror problem by considering
the two types of frame of reference: the intrinsic frame of reference (IFR) and the
common frame of reference (CFR). There is an IFR that belongs to the object and one
1050
H Yoshimura, T Tabata
that belongs to its mirror image, and each IFR is applied to the object and its mirror
image separately (hereafter we call this simply ``the application of the IFR''). The
CFR is applied simultaneously to the object and its mirror image. Ittelson et al (1991),
Corballis (2000), Tabata and Okuda (2000), and McManus (2002) referred in various
ways to this IFR ^ CFR dichotomy. Ittelson et al (1991) pointed out that the study of
mirror perception must take into account the two different sets of axes öthe physical
system fixed with respect to the stable features of the world and the object system fixed
with respect to the object. Corballis (2000) called these two systems an environmentcentred reference system and an object-centred one; the former is similar to our CFR,
and the latter is the same as our IFR. Tabata and Okuda (2000) proposed a solution
to the mirror puzzle by selecting the coordinate system inherent to the object and its
mirror image, ie the IFR in our definition. McManus (2002) also proposed a solution
to the mirror puzzle by applying the principle of axis-determination order (this principle
is explained in the next section) to the top ^ bottom, front ^ back, and right ^ left of a
mirror image, similarly to Corballis (2000) and Tabata and Okuda (2000). However,
none of these authors referred to the critical roles of different coordinate systems in
different perceptions of mirror images.
3 Approach to extended mirror problem
3.1 IFR and left ^ right reversal
The human body and many ordinary objects have built-in (intrinsic) asymmetry in
the top ^ bottom and front ^ back directions, but are approximately symmetric in the
left ^ right direction. Thus, it is an established practice that only after the top ^ bottom
and front ^ back axes have been identified, is the third axis, left ^ right, fixed in
applying an IFR. This practice is here termed the principle of axis-determination
order.
When we are looking into a mirror, the principle of axis-determination order is
used to match first top ^ bottom and front ^ back axes between the body and its mirror
image, ie between the enantiomorphs, in order to compare their shapes. This corresponds to the application of an IFR to each, the object and its mirror image. As a
result, we are forced to perceive that the direction reversed in the mirror image is the
direction compared last in order, ie the left ^ right direction (Corballis 2000; Tabata
and Okuda 2000; McManus 2002).
The above explanation holds true not only for solid objects but also for an asymmetric letter written on a sheet of paper. While the front ^ back axis of a letter is
unclear, we can identify it by regarding the surface of the sheet of paper where the
letter is written as the front and the reverse as the back. According to this reasoning,
we can also explain the left ^ right reversal of an asymmetric letter in the same manner
as that of asymmetric solid objects (Tabata and Okuda 2000).
Therefore, the original mirror puzzle: ``Why does the mirror reverse left and right,
but not up and down?'' can be considered implicitly to assume the application of the
IFR, as noted by Corballis (2000) and Tabata and Okuda (2000). Thus, we can
conclude that the application of the IFR always leads to the perception of left ^ right
reversal so far as the object has left ^ right asymmetry (left ^ right asymmetry is the
necessary condition for the perception of left ^ right reversal).
3.2 Examples of left ^ right nonreversal
From the relationship between the perception of left ^ right reversal and the IFR, we
can infer that the perception of left ^ right nonreversal is related to the application of
a CFR to the object and its mirror image. On the basis of this assumption, let us
consider typical examples in which we perceive left ^ right nonreversal:
Relationship between frames of reference and mirror-image reversals
1051
Example 1. Standing before a floor mirror, almost all persons say that their image is
reversed in the up ^ down direction.
Example 2. Some persons do not perceive left ^ right reversal in their mirror images
with the right hand raised, for example, and state that the mirror image also raises the
right(-side) hand.
Example 3. When seeing a motorbike shifting to its left in the rearview mirror of a
car, a driver does not perceive left ^ right reversal, ie she/he observes the image of the
motorbike as moving leftward, and identifies the movement correctly in real space
(see figure 1).(1)
Figure 1. A motorbike in the rearview mirror of a car. A common frame of reference is applied to
the real and mirror spaces.
Example 4. When applying make-up in front of a mirror, women do not make errors
in penciling their eyebrow from left to right.
Example 5. There are objects that have none of top ^ bottom, front ^ back, and left ^
right intrinsic axes. An example is the three-dimensional object made of seven cubes
used in the mental rotation paradigm developed by Shepard and Metzler (1971) (see
figure 2). The importance of this example is that the seven-cube object does not have
any intrinsic orientation in spite of being asymmetric in all the three orthogonal axes
taken along the edges of the cubes. Except when this object is reflected by the side
mirror, we do not perceive the left ^ right reversal of its mirror image. Thus, when the
object is reflected by the front mirror, it is perceived as front ^ back reversed; and when
reflected by the floor mirror as top ^ bottom reversed.
(1) When the left flashing indicator of the motorbike coming from his/her backside is on, the
driver of the car will properly perceive that the left-side indicator is flashing according to the CFR.
However, the driver may as well say that the right flashing indicator of the motorbike is on by
applying an IFR to the image of the motorbike. The presence of the latter response does not
invalidate the adequacy of example 3.
1052
H Yoshimura, T Tabata
Figure 2. Three-dimensional objects made of seven cubes reflected in front, floor, and side
mirrors. Mirror images are perceived to be reversed in the front ^ back, top ^ bottom, and left ^ right
directions.
Example 6. Some ordinary objects have only a single intrinsic axis in either the top ^
bottom or the front ^ back direction. For example, an arrow (figure 3a) has the intrinsic
front ^ back but not the top ^ bottom, and a nonpatterned cup (figure 3b) has the
intrinsic top ^ bottom but not the front ^ back axis. Looking at the image of these
objects in a front mirror, we never perceive them as left ^ right reversed, unlike the
case of the object with three intrinsic axes. This might sound trivial, but makes it clear
that the perception of left ^ right reversal needs all the three intrinsic axes.
(a)
(b)
Figure 3. Examples of objects having only one intrinsic axis. (a) An arrow and its mirror image;
a case having only intrinsic front ^ back. (b) A cup and its mirror image; a case having only
intrinsic top ^ bottom.
Example 7. Consider the case in which a woman with a mole on the right cheek wants
to confirm on which cheek the mole is located by looking into a mirror. Although
the mirror image has the mole on its left cheek, she instantly finds that the mole is
Relationship between frames of reference and mirror-image reversals
1053
on her right cheek without giving any consideration to the left ^ right reversal of her
mirror image.(2)
3.3 CFR and left ^ right nonreversal
When a woman states that the mirror image of her body is not left ^ right reversed
(examples 1 and 2), she is applying a single observer-centred frame of reference that is
common to real and mirror spaces. As mentioned earlier, we term this frame of reference common frame of reference (CFR). Similarly, when looking at a motorbike in
the rearview mirror of a car (example 3), a driver applies a CFR for the real and
mirror worlds as shown in figure 1. When applying make-up in front of a mirror
(example 4), women also identify the left ^ right and top ^ bottom directions by the use
of a CFR. Relying on the CFR, they do not perceive either left ^ right or top ^ bottom
reversal, but are prompted to perceive front ^ back reversal as the logical consequence
of enantiomorphism.
The IFR cannot be applied to objects without an intrinsic axis (example 5) or to
those that have only a single intrinsic axis (example 6). Therefore, we are compelled
to use a CFR for these objects. In example 7, the woman who perceives left ^ right
nonreversal also relies on a CFR.
As mentioned above, the application of a CFR leads to nonreversal in the left ^
right axis in most cases. In some cases, however, it can lead to left ^ right reversal,
one of the examples of which is the three-dimensional object made of seven cubes
reflected by the side mirror in example 5.
3.4 What CFR generally causes
The direct consequence of the application of a CFR is not the nonreversal of the
left ^ right axis, but simply the reversal of the axis normal to the mirror, according to
geometrical optics. Examples 1 to 7 indicate that the left ^ right axis does not coincide
with the axis normal to the mirror in most practical cases, in which one perceives the
left ^ right nonreversal of the mirror image. On the other hand, when the normal to
the mirror happens to be the left ^ right axis of the CFR adopted, the mirror image is
perceived as left ^ right reversed.
Psychologically, a CFR can be based on one of the three types of orientation
pointed out by Rock (1973): the environmental orientation, the egocentric orientation, and the intrinsic orientation of an object. In example 5, the CFR adopted would
naturally be based on the egocentric orientation of the observer. In the side-mirror
case of example 5, therefore, the left ^ right axis of the CFR coincides with the axis
normal to the mirror, and left ^ right reversal is perceived in the mirror image. Similarly, left ^ right reversal is perceived also when the left ^ right axis of the CFR based
on either the environmental orientation or intrinsic orientation of the object coincides
with the axis normal to the mirror.
Thus, we can say that the perception of left ^ right nonreversal is due to the application of a CFR, but we cannot say that the application of a CFR always leads
to left ^ right nonreversal as explained above. The relationship between the perception
of left ^ right reversal or nonreversal and the application of the IFR or CFR can be
drawn as a Venn diagram, as shown in figure 4. Areas A and B are clear, and we
have also explained the occurrence of the cases that belong to area C.
Despite classifying the basis of mirror-image perception as the use of the CFR
and IFR, we still allow the application of both kinds of frames of reference, and the
application of a set of CFRs based on different orientations, to a single scene in a
single instant. Applying make-up in the mirror, for example, a woman may well move
(2) A
different response based on the use of IFR may also happen, but it cannot affect the perception
of left ^ right nonreversal in this example.
1054
H Yoshimura, T Tabata
left ± right
nonreversal
left ± right
reversal
application of CFR
B
C
application of IFR
A
Figure 4. Relationship between the perception of left ^
right reversal and the application of the IFR or CFR.
the pencil left to right and top to bottom in accordance with what she sees in the
mirror, controlled by a CFR. At the same time, she may notice that the writing on her
T-shirt is left ^ right reversed. This is controlled by the IFR. We find a similar example
of the dual control of frames of reference in a single scene in the context of a left ^ right
visual reversal experiment. Kohler (1964) wrote about a subject's report of strange
impression when wearing a left ^ right reversing device:
``Inscriptions on buildings, or advertisements, were still seen in mirror writing, but the
objects containing them were seen in the correct location. Vehicles driving on the `right'
(and the noise of the motor agreed) carried license numbers in mirror writing.'' (page 155)
Harris (1965) took this seriously and named it piecemeal adaptation. Thus our
perceptual system may apply CFR and IFR simultaneously to objects or things in the
same scene. It can also apply them to mirror images. Moreover, when we are looking
at a mirror, there is a tendency for the locations of things to be perceived on the basis
of CFR and the shapes of objects to be perceived under the control of IFR. However,
this may not always be true, so that we do not say that this is a rule in mirror-image
perception.
4 Concluding remarks
Our treatment of the extended mirror problem is based on the solution given by
Corballis (2000), Tabata and Okuda (2000), and McManus (2002) to the original mirror
puzzle. This solution has not met with any substantial and effective counterargument
since its publication, and can be considered to have superseded all the previous hypotheses about the original puzzle, giving a firm foundation to the present treatment. (3)
Ittelson et al (1991) also pointed out the ambiguity of the mirror puzzle, but
resolved it in a manner different from ours. They reformulated the puzzle into physical
and perceptual problems, thus treating only the original mirror puzzle without extending it. They concluded that the perception of reversal occurs along the specific axis of
the least perceived asymmetry (or greatest perceived symmetry), but their hypothesis
was severely criticised by Corballis (2000). Therefore the analysis and conclusions of
Ittelson et al are fundamentally different from ours despite apparent similarities between
some of their descriptions and ours.
To predict exactly if an observer perceives left ^ right reversal or nonreversal of the
mirror image under any situation, it is necessary to clarify the observer's psychological preferences for the IFR or CFR (with one of Rock's three orientation bases)
in every conceivable type of situation. This would be a difficult problem that might not
have a clear-cut solution because of the flexibility and insecurity of mental processes.
(3)
One of the reviewers of this paper told us that Morgan's book (2003) already included a comprehensive solution to the original mirror puzzle, but we do not think so. Morgan's explanation of
mirror reversal is quite similar to Gregory's (1987, 1997). The explanations of these two authors are
criticised in the Appendix.
Relationship between frames of reference and mirror-image reversals
1055
Therefore, the first critical step for understanding the extended mirror problem is the
clarification of the physical conditions that lead to the left ^ right reversal and nonreversal. In the present study, this task was performed logically and parsimoniously.
References
Corballis M C, 2000 ``Much ado about mirrors'' Psychonomic Bulletin & Review 7 163 ^ 169
Gardner M, 1964 The Ambidextrous Universe (New York: Basic Books)
Gardner M, 1990 The New Ambidextrous Universe 3rd revised edition (New York: W H Freeman)
Gregory R L, 1987 ``Mirror reversal'', in The Oxford Companion to the Mind Ed. R L Gregory
(Oxford: Oxford University Press) pp 491 ^ 493
Gregory R L, 1997 Mirrors in Mind (New York: W H Freeman)
Harris C S, 1965 ``Perceptual adaptation to inverted, reversed, and displaced vision'' Psychological
Review 72 419 ^ 444
Ittelson W H, Mowafy L, Magid D, 1991 ``The perception of mirror-reflected objects'' Perception
20 567 ^ 584
Kohler I, 1964 ``The formation and transformation of the perceptual world'' Psychological Issues
3 1 ^ 173
McManus I C, 2002 Right Hand, Left Hand: The Origins of Asymmetry in Brains, Bodies, Atoms
and Cultures (London: Weidenfeld & Nicolson)
Morgan M, 2003 The Space between Our Ears: How the Brain Represents Visual Space (London:
Weidenfeld & Nicolson)
Rock I, 1973 Orientation and Form (New York: Academic Press)
Shepard R N, Metzler J, 1971 ``Mental rotation of three-dimensional objects'' Science 171 701 ^ 703
Southall J P C, 1933/1964 Mirrors, Prisms and Lenses: A Textbook of Geometrical Optics 3rd edition
(New York: Dover)
Tabata T, Okuda S, 2000 ``Mirror reversal simply explained without recourse to psychological
processes'' Psychonomic Bulletin & Review 7 170 ^ 173
Appendix
Here we criticise Gregory's and Morgan's explanations of mirror reversals by comparing
them with our treatment.
Gregory (1987) writes,
``The mirror reflects top as top, bottom as bottom, right as right, and left as left: the mirror
does not reverse right to left or up to down.''
According to our treatment, this is a correct description so far as the use of a CFR
is assumed. To observe left ^ right reversal, it is necessary to use an IFR for each of
the object and its mirror image, ie a pair of enantiomorphs. Gregory's explanation
lacks this step of elucidating the essence of left ^ right reversal. Thus it is unclear what
he means by `these mirror reversals' in his answer:
``In all cases, it is object rotation that produces these mirror reversals in plane mirrors.''
Gregory possibly considers the mirror image of the text seen in `mirror writing' to
be an example of left ^ right reversal, but he strangely and wrongly denies the appearance of mirror writing in one case by writing:
``When, for example, a book is rotated around its horizontal axis to face a mirror, it appears
upside-down, and not in `mirror writing'.''
After rotation around a horizontal axis, the text in the mirror surely runs from left
to right as you saw in the real book before rotation. However, he fails to note that the
mirror image of each asymmetric letter is a `mirror letter' just like the case of rotation
of the book around a vertical axis, and that the text in the mirror is actually mirror
writing seen upside-down. Thus Gregory fails to explain the constant occurrence of
mirror writing in a mirror.
1056
H Yoshimura, T Tabata
Gregory (1997) makes the same error about the mirror image of ourselves by stating:
``A mirror shows us ourselves right ^ left reversed (reversed from how others see us without
the mirror) because we have to turn around to face it. ... But we can face the mirror by
standing on our headöthen, we are upside down in the mirror and not left ^ right reversed.''
Here he gives a short explanation of what he means by `right ^ left reversed', but he
again fails to notice that the same right ^ left reversal is also seen when we stand on
our head. Thus Gregory's hypothesis based on object rotation is far from being a valid
solution to the original mirror problem. In our treatment, the occurrence of left ^ right
reversal in mirror images in any relative configuration of asymmetric objects (including
letters) with respect to a mirror can be explained as described in subsection 3.1 of the
present paper.
Morgan (2003) explains the reversal of the mirror image of a text in the same
manner as Gregory. The latter author attributed all the reversals to physical rotation,
but Morgan has a somewhat different view about the reversal of the mirror image
of ourselves, attributing it to mental rotation and making the hypothesis complicated
without any improvement.
Morgan includes a consideration of an unusual case of looking at the image of a
book in a mirror through our legs, and writes,
``The text is no longer left ^ right reversed... Close inspection reveals that it is upside down.''
The text is actually left ^ right reversed in the sense that it is in mirror writing, but
Morgan misses this, following Gregory. In contradiction to the above passage, Morgan
also writes:
``[T]he impression of the writer is that objects such as chairs do not seem upside down
[when looked at through our legs].''
This confusion comes from his lack of discrimination between the possible bases of
the CFR, the environmental and egocentric orientations, in speaking of the up ^ down
direction. In our treatment, the possible three bases of the CFR mentioned by Rock
(1973) can naturally be accommodated as discussed in subsection 3.4.
ß 2007 a Pion publication
ISSN 0301-0066 (print)
ISSN 1468-4233 (electronic)
www.perceptionweb.com
Conditions of use. This article may be downloaded from the Perception website for personal research
by members of subscribing organisations. Authors are entitled to distribute their own article (in printed
form or by e-mail) to up to 50 people. This PDF may not be placed on any website (or other online
distribution system) without permission of the publisher.